Problem: The grades on a history midterm at Gardner Bullis are normally distributed with $\mu = 69$ and $\sigma = 3.5$. Ishaan earned a $65$ on the exam. Find the z-score for Ishaan's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ishaan's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{65 - {69}}{{3.5}}} $ ${ z \approx -1.14}$ The z-score is $-1.14$. In other words, Ishaan's score was $1.14$ standard deviations below the mean.